TRANSFORMATION INVARIANCE OF THE LONGITUDINAL VELOCITY CORRELATION IN GRID-GENERATED TURBULENCE AT HIGH REYNOLDS NUMBERS.

For grid Reynolds numbers from 12800 to 81000, the F. N. Frenkiel-P. S. Klebanoff-T. T. Huang data for approximately isotropic homogeneous grid-generated turbulence shows that the longitudinal correlation function is given by the simple empirical expression f equals left bracket 1 plus (r/2L) right bracket ** minus **3, where r ( VM GT TH 0. 01 M) is the separation distance between two points in the fluid flow and L equals L(t) is the integral scale. It follows that the longitudinal velocity correlation LT AN BR u//1(x plus re, t) u//1(x, t) RT AN BR equals u**2f with e equals (1, 0, 0) is invariant under the separation-distance time-contraction transformations r yields left bracket r plus (1 minus lambda )2L right bracket , t lambda 5/2 t for all positive parameter values lambda less than equivalent to 1. Conversely, if the longitudinal correlation function is prescribed to have the form f equals F(r/L(t), then the indicated transformation invariance holds if and only if F ( xi ) equals (1 plus one-half xi )** minus **3. It is also shown that a Gaussian normal probability distribution at t equals 0 and the Karman-Howarth equation for all t greater than 0 are compatible with the transformation invariance and associated expression for f.